In the paper Existence de processus Markoviens pour des systèmes infinis de particules by Cocozza, C. and Kipnis, C. (Ann. lnst. H. Poincaré, Sect. B, 13, 239-257, 1977), one reads
If $m^x \in \mathcal{M}^1$ what is the meaning of $m^x]0,k]$
Isn't $m^x]0,k] = m^x]0,1]$?
There is a typo here, $m^x$ should be an element of $ \mathcal{M}(\Bbb{R}_+)$, then the definitions make sense.